From Zero to Infinity

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Short description: Number theory book

From Zero to Infinity: What Makes Numbers Interesting is a book in popular mathematics and number theory by Constance Reid. It was originally published in 1955 by the Thomas Y. Crowell Company.[1] The fourth edition was published in 1992 by the Mathematical Association of America in their MAA Spectrum series.[2][3][4] A K Peters published a fifth "Fiftieth anniversary edition" in 2006.[5][6][7][8][9][10]

Background

Reid was not herself a professional mathematician, but came from a mathematical family that included her sister Julia Robinson and brother-in-law Raphael M. Robinson.[11] She had worked as a schoolteacher, but by the time of the publication of From Zero to Infinity she was a "housewife and free-lance writer".[1] She became known for her many books about mathematics and mathematicians, aimed at a popular audience, of which this was the first.[11]

Reid's interest in number theory was sparked by her sister's use of computers to discover Mersenne primes. She published an article on a closely related topic, perfect numbers, in Scientific American in 1953, and wrote this book soon afterward.[4] Her intended title was What Makes Numbers Interesting; the title From Zero to Infinity was a change made by the publisher.[8]

Topics

The twelve chapters of From Zero to Infinity are numbered by the ten decimal digits, [math]\displaystyle{ e }[/math] (Euler's number, approximately 2.71828), and [math]\displaystyle{ \aleph_0 }[/math], the smallest infinite cardinal number. Each chapter's topic is in some way related to its chapter number, with a generally increasing level of sophistication as the book progresses:[4][5][10]

The first edition included only chapters 0 through 9.[1] The chapter on infinite sets was added in the second edition, replacing a section on the interesting number paradox.[12] Later editions of the book were "thoroughly updated" by Reid;[4] in particular, the fifth edition includes updates on the search for Mersenne primes and the proof of Fermat's Last Theorem, and restores an index that had been dropped from earlier editions.[9]

Audience and reception

From Zero to Infinity has been written to be accessible both to students and non-mathematical adults,[4] requiring only high-school level mathematics as background.[7] Short sets of "quiz questions" at the end chapter could be helpful in sparking classroom discussions, making this useful as supplementary material for secondary-school mathematics courses.[6][10]

In reviewing the fourth edition, mathematician David Singmaster describes it as "one of the classic works of mathematical popularisation since its initial appearance", and "a delightful introduction to what mathematics is about".[4] Reviewer Lynn Godshall calls it "a highly-readable history of numbers", "easily understood by both educators and their students alike".[6] Murray Siegel describes it as a must have for "the library of every mathematics teacher, and university faculty who prepare students to teach mathematics".[10]

Singmaster complains only about two pieces of mathematics in the book: the assertion in chapter 4 that the Egyptians were familiar with the 3-4-5 right triangle (still the subject of considerable scholarly debate) and the omission from chapter 7 of any discussion of why classifying constructible polygons can be reduced to the case of prime numbers of sides.[4] Siegel points out another small error, on algebraic factorization, but suggests that finding it could make another useful exercise for students.[10]

References

  1. 1.0 1.1 1.2 Gibb, E. Glenadine (February 1957), "Review of From Zero to Infinity, 1st ed.", The Mathematics Teacher 50 (2): 178 
  2. Leamy, John (March 1993), "Review of From Zero to Infinity, 4th ed.", The Mathematics Teacher 86 (3): 265 
  3. "Review of From Zero to Infinity, 4th ed.", Scientific American 267 (6), December 1992 
  4. 4.00 4.01 4.02 4.03 4.04 4.05 4.06 4.07 4.08 4.09 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 "Review of From Zero to Infinity, 4th ed.", MathSciNet, 1993 
  5. 5.00 5.01 5.02 5.03 5.04 5.05 5.06 5.07 5.08 5.09 5.10 Belle, Vaishak (June 2011), "Review of From Zero to Infinity, 5th ed.", ACM SIGACT News 42 (2): 10–11, doi:10.1145/1998037.1998040, https://www.cs.umd.edu/~gasarch/bookrev/42-2.pdf 
  6. 6.0 6.1 6.2 Godshall, Lynn (July 2007), "Review of From Zero to Infinity, 5th ed.", Convergence, https://www.maa.org/press/periodicals/convergence/from-zero-to-infinity 
  7. 7.0 7.1 Hoagland, Kayana (April 2008), "Review of From Zero to Infinity, 5th ed.", The Mathematics Teacher 101 (8): 622–623 
  8. 8.0 8.1 Lozano-Robledo, Álvaro (May 2006), "Review of From Zero to Infinity, 5th ed.", MAA Reviews (Mathematical Association of America), https://www.maa.org/press/maa-reviews/from-zero-to-infinity-what-makes-numbers-interesting 
  9. 9.0 9.1 Papp, F.-J. (2006), "Review of From Zero to Infinity, 5th ed.", MathSciNet 
  10. 10.0 10.1 10.2 10.3 10.4 10.5 10.6 Siegel, Murray H. (February 2007), "Review of From Zero to Infinity, 5th ed.", Mathematics Teaching in the Middle School 12 (6): 350 
  11. 11.0 11.1 "Author and longtime MAA member Constance Reid dies at 92", MAA News (Mathematical Association of America), October 20, 2010, https://www.maa.org/news/math-news/author-and-longtime-maa-member-constance-reid-dies-at-92 
  12. Hamilton, J. M. C. (1960), "Review of From Zero to Infinity, 2nd ed.", Mathematics Magazine 34 (1): 43–44, doi:10.2307/2687853